How many types of variational auto-encoders are there?
There are many variations of the original VAE (proposed in the 2013 paper Auto-Encoding Variational Bayes), with different purposes (such as the generation of discrete data or graphs). Of course, I cannot enumerate all of them, so here I will list only the ones I am currently aware of.

Conditional variational auto-encoder (CVAE) (2015, NeurIPS)
Adversarial autoencoders (AAE) (2015, ICLR)
Ladder variational autoencoder (LVAE) (2016,  NeurIPS)
VAE/GAN (2016, PMLR)
Vector quantised variational autoencoder (VQ-VAE) (2017, NeurIPS)
Denoising variational autoencoder (DVAE) (2017, AAAI)
Grammar variational autoencoder (GVAE) (2017, ICML)
Syntax-directed variational autoencoder (SD-VAE) (2017, ICLR)
PixelVAE (2017)
GraphVAE (2018, ICANN)
Constrained graph variational autoencoder (CGVAE) (2018, NeurIPS)
Character VAE (CVAE) (2018, ACS central science)
Regularized VAE (RVAE) (2018, NeurIPS)
Junction tree variational autoencoder (JT-VAE) (2018, PMLR)
InfoVAE/MMD-VAE (2019, AAAI)
Molecular hypergraph grammar variational autoencoder (MHG-VAE) (2019, ICML)
DAG variational autoencoder (D-VAE) (2019, NeurIPS)
Denoising adversarial autoencoders (iDAAE and DAAE) (2019, IEEE Transactions on Neural Networks and Learning Systems)
MACRo-mIcro Disentangled Variational Auto-Encoder (MacridVAE) (2019, NeurIPS)

VAEs have been used for drug design (see e.g. JT-VAE) and in reinforcement learning (see e.g. world models). I don't know if they have been used for self-driving cars, but it's possible.